Not to be too weird, but the gold standard for that very specific use case is a box cutter. No modifications required, very normal to have in about a thousand different blue collar jobs, costs like five bucks, and will absolutely fillet a human if you're inclined for some reason.
I suspect anyone found with one of those in the street by Her Majesty's constabulary would have some explaining to do, unless they could prove they were a carpet-fitter on their way to a job. The laws on 'offensive weapons' are pretty strict.
Though I do, personally, suspect there's too much emphasis in the media on the idea that teens stab each other (which they do on a frequent basis in this city) because they just happened to have a weapon on them and decided to use it on the spur of the moment.
As far as I can see, many such stabbings happen because the stabber took a weapon with them with the specific intent to stab someone. Thus random stop-and-searches would seem to have a low-chance of catching the perps before they kill.
I'm very happy guns are not commonplace, though. It seems like it takes a much stronger motivation to stab someone than to shoot them. I've a couple of times in my life had someone try to mug me at knifepoint, and both times they eventually gave up and ran off when I wouldn't co-operate. I strongly suspect those incidents would have gone very differently if they'd had a gun.